On the continuation principles for the Euler equations and the quasi-geostrophic equation (Q2498848)

The paper deals with the homogeneous incompressible Euler equation in \(\mathbb{R}\): \[ \frac{\partial v}{\partial t}+(v\cdot\nabla)v=-\nabla p, \] \[ \text{ div}\,v=0, \] \[ v(x,0)=v_0(x), \] where \(v\) is the velocity of the fluid flows, \(p=p(x,t)\) is the scalar pressure, \(v_0(x)\) is a given initial velocity field satisfying \(\text{ div}\,v_0=0\). A continuation principle of the local classical solutions is obtained. A similar result for the inviscid 2D quasi-geostrophic equation is also obtained.